Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of <Emphasis Type="Italic">β</Emphasis>-stable <Emphasis Type="Italic">npeμ</Emphasis> matter

Momentum and density dependence of single-nucleon potential u_τ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even–even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number 160 ≤ N ≤ 204 are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter η and the relative neutron–proton asymmetry of the surface to the center (R _η ) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter η and the relative neutron–proton asymmetry R _η of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface, facets a superheavy nucleus for β^? decays.     

Fine Structure of Beta Decay Strength Function and Anisotropy of Isovector Nuclear Dencity Component Oscillations in Deformed Nuclei

The experimental measurement data on the fine structure of beta-decay strength function S_β(E) in spherical, transitional, and deformed nuclei are analyzed. Modern high-resolution nuclear spectroscopy methods made it possible to identify the splitting of peaks in S_β(E) for deformed nuclei. By analogy with splitting of the peak of E1 giant dipole resonance (GDR) in deformed nuclei, the peaks in S_β(E) are split into two components from the axial nuclear deformation. In this report, the fine structure of S_β(E) is discussed. Splitting of the peaks connected with the oscillations of neutrons against protons (E1GDR), of proton holes against neutrons (peaks in S_β(E) of β⁺/EC-decay), and of protons against neutron holes (peaks in S_β(E) of β^–-decay) is discussed.     

Die Kernradiusänderung beim Einbau eines Protons

The change of therms radius of the nuclear charge distribution on addition of one proton is derived for 25 nuclides between ₁₉ ³⁹ K and ₈₂ ²⁰⁸ Pb. For this purpose, results of the muonic 2p-1s transition energies are used together with the optical isotope shifts. The uncertainties of the procedure are discussed. Corresponding results from elastic electron scattering are included for three pairs of nuclides. — For heavy nuclei, the average increase in radius per proton exceeds considerably that per neutron, as expected. Although the individual values are associated with rather large errors, shell effects seem to be noticeable atZ=28 andZ=50.     

Forward particle production in proton–nucleus interactions at momenta of 25 and 50 GeV/<Emphasis Type="Italic">с</Emphasis> and сarbon–nucleus interactions at an energy of 25 GeV per nucleon

Relative yields of high-x _F charged hadrons (π ^±, К^±, р, \(\overline p \), and d) in proton–nucleus interactions at incident-proton momenta of 25 and 50 GeV/c were measured at an angle of 0° in the momentum range between 15 and 40 GeV/c. An upper limit on the forward production of two protons in proton–nucleus interactions at 50 GeV/c was estimated. The properties of a carbon beam with an energy of 25 GeV per nucleon and fragment yields in its interaction with nuclear targets were measured within a short exposure.     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

Experimental investigation of ρ<Superscript>0</Superscript> photoproduction on the pion in the H1 experiment

Experimental results on quasielastic photoproduction of the ρ⁰ meson in association with a neutron, obtained at the HERA collider, are presented. The total and differential cross sections of the γp → ρ⁰ nπ⁺ reaction at the positron–proton center-of-mass energy of √s =319 GeV are measured. The data collected with the H1 detector in 2006 and 2007 correspond to an integrated luminosity of 1.16 pb^?1. The kinematic region of the photon–proton cms energy of 20 < W _γp <100 GeV, photon virtuality of Q ² < 2 GeV², and the ρ⁰ transverse momentum below 1 GeV/c is analyzed. Secondary neutrons with energies x _L > 0.35 (in proton-energy units) and emission angles below 0.75 mrad are selected. The model of double peripheral exchange, in which the ρ⁰ is elastically produced via the photon interaction with the virtual pion from the proton–neutron vertex, is employed for interpreting the results. The cross section for the ρ⁰ elastic photoproduction on the pion, γπ⁺→ ρ⁰π⁺, is extracted in the one-pion-exchange approximation. The magnitude of the cross section suggests that the γp → ρ⁰ nπ⁺ reaction is significantly affected by absorption.     

Inclusive pion production by pions on nuclei and determination of root-mean-square radii of proton and neutron distributions

A brief nonanalytic survey of data available in the literature for parameters that characterize nuclear sizes is given, and the potentials of some methods for determining these sizes are compared. Attention is given primarily to determining nuclear sizes in experiments that study pion-nucleus interaction. For pointlike protons and neutrons, values of parameters that describe the radial dependences of their densities according to the Fermi distribution are presented in a tabular form. The method proposed previously at the Institute of Theoretical and Experimental Physics (ITEP, Moscow) for determining nuclear sizes on the basis of measuring differential cross sections for π^? + A → π _forw ^± + X processes in the kinematical region where the recorded interaction event occurs on a single proton (neutron) of nucleus A, the presence of the remaining nucleons manifesting itself in shadowing effects, is described, and examples of the application of this method are given.     

Diffraction enhancement effect and new possibilities of measuring the electric charge of the neutron and its inertial-to-gravitational mass ratio

Diffraction enhancement of small effects affecting a neutron undergoing Laue diffraction at Bragg angles θ _B close to 90° is predicted and experimentally observed. The enhancement is due to the delay of the neutron inside the crystal during diffraction and is proportional to tan² θ _B. As a result, the diffraction enhancement factor may be as large as ～10⁸–10⁹. On this basis, a new method is proposed for searching for the electric charge of the neutron and for measuring the ratio of its inertial mass m _i to the gravitational mass m _G . It is shown that the accuracy of the neutron charge measurement can be improved by more than two orders of magnitude in relation to the present-day accuracy and that the ratio m _i /m _G can be measured to an precision of σ(m _i /m _G ) ～ 10^?6.     

Theory of the muonic hydrogen-muonic deuterium isotope shift

Corrections of the α³, α⁴, and α⁵ orders are calculated for the Lamb shift of the 1S and 2S energy levels of muonic hydrogen μp and muonic deuterium μd. The nuclear structure effects are taken into account in terms of the charge radii of the proton r _p and deuteron r _d for one-photon interaction, as well as in terms of the electromagnetic form factors of the proton and deuteron for the case of one-loop amplitudes. The μd-μp isotope shift for the 1S-2S splitting is found to be equal to 101003.3495 meV, which can be treated as a reliable estimate when conducting the corresponding experiment with an accuracy of 10^?6. The fine-structure intervals E(1S)-8E(2S) in muonic hydrogen and muonic deuteron are calculated.     

Schiff moment of the mercury nucleus and the proton dipole moment

The Schiff moment of the ¹⁹⁹Hg nucleus is calculated using finite range P-and T-violating weak nucleon-nucleon interaction. Both the contributions of the P-and T-odd interaction and of internal nucleon electric dipole moments to the Schiff moment of ¹⁹⁹Hg are calculated. The contribution of the proton electric dipole moment is obtained via core-polarization effects treated in the framework of RPA with effective residual interactions. We derive a new upper bound |d _p |<5.4×10^?24e cm for the proton electric dipole moment.     

Viscosity Correlations with Nuclear (Proton) Magnetic Resonance Relaxation in Oil Disperse Systems

Using nuclear (proton) magnetic resonance relaxometry (NMRR) was studied oil disperse systems. Dependences of NMR–relaxation parameters—spin–lattice T_1i, spin–spin T_2i relaxation times, proton populations P_1i and P_2i, and petrophysical correlations were received for light and heavy oils. Experimental results are interpreted on the base of structure-dynamical ordering of oil molecules with structure unit formation.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Dual origin of pairing in nuclei

The pairing correlations of the nucleus ¹²⁰Sn are calculated by solving the Nambu–Gor’kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong ¹ S ₀ short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v _p ^bare) and long-range (v _p ^ind) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.     

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at g_π²±/4π = 14.55(13). This value is in perfect agreement with the experimental value of g_π²±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is g_π² 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.     

Homogeneous nucleation in liquid nitrogen at negative pressures

The kinetics of spontaneous cavitation in liquid nitrogen at positive and negative pressures has been studied in a tension wave formed by a compression pulse reflected from the liquid–vapor interface on a thin platinum wire heated by a current pulse. The limiting tensile stresses (Δp = p_s–p, where p_s is the saturation pressure), the corresponding bubble nucleation frequencies J (10²⁰–10²² s^–1 m^–3), and temperature induced nucleation frequency growth rate G_T = dlnJ/dT have been experimentally determined. At T = 90 K, the limiting tensile stress was Δp = 8.3 MPa, which was 4.9 MPa lower than the value corresponding to the boundary of thermodynamic stability of the liquid phase (spinodal). The measurement results were compared to classical (homogeneous) nucleation theory (CNT) with and without neglect of the dependence of the surface tension of critical bubbles on their dimensions. In the latter case, the properties of new phase nuclei were described in terms of the Van der Waals theory of capillarity. The experimental data agree well with the CNT theory when it takes into account the “size effect.”     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Measurement of polarization angular coefficients in <Emphasis Type="Italic">Z</Emphasis> boson leptonic decays with ATLAS at the LHC

This paper presents the complete set of polarization angular coefficients A _0?7 describing lepton angular distributions in Z boson decay, which were measured at the ATLAS experiment in proton–proton collisions with the energy √s = 8 TeV. Theoretical values for the difference A ₀ ? A ₂ calculated in the fixed-order QCD perturbation theory O(α _s ² ), demonstrate significant deviation from the measured data, which indicates the necessity of taking into account higher order corrections. The evidence of nonzero coefficients A _5,6,7 was obtained for the first time, in accordance with theoretical calculations in O(α _s ² ) approximation. Measurement of the polarization angular coefficients A _i is important for subsequent precision measurement of parameters of the electroweak model at the LHC, such as the sine of Weinberg electroweak mixing angle sin² θ _W and the W boson mass.